Convolutional Neural Networks and Classification

Classification

• Regression:
  • output is a prediction on a quantity which takes continuous values
• Classification:
  • output is a prediction on a class, i.e. discrete labels
    • binary classification
    • multi-class classification
      • single-label classification
      • multi-label classification

Convolutional Neural Network (CNN, ConvNet)

• a class of artificial Neural Networks
• widely used in computer vision*
• learn hierarchy of features

*Computer vision is an essential, complex, wide-spread, and ever developing part of AI. Computer vision tasks include:

• Image Classification
• Classification with localization
• Object detection (verify the presence of specific objects in an image)
• Semantic segmentation
• Instance segmentation
• Neural Style Transfer

Why CNNs?

Image of 1300 X 1300px --> Input on a layer of a FC (Dense) network with e.g. 1000 hidden units -->

parameters (weights) to calculate : (1000,1300x1300) = 1.69E9 parameters (x3 for a color image)

\textbf{Create some simple 3x3 filters and apply with a convolution operator on images }

Convolution Operation

Example with edges filters

filter_v=np.array([[1,0,-1],[1,0,-1],[1,0,-1]])  # 3x3 vertical edges filter 
filter_h=np.array([[1,1,1],[0,0,0],[-1,-1,-1]])  # 3x3 horizontal edges filter 
filter_v_3d=np.dstack([filter_v]*3)                 # 3x3x3 vertical edges filter 
filter_h_3d=np.dstack([filter_h]*3)                 # 3x3x3 horizontal edges filter 

Apply edge detector on gray scale image (nh x nw)

image = Image.open('brick2.jpeg').convert('L')
brick = asarray(image)
plt.figure(figsize=(10,10))
plt.imshow(brick,cmap='gray')
plt.axis('off')
plt.show()

out_conv_h=signal.convolve2d(brick,filter_h,mode='valid')
out_conv_v=signal.convolve2d(brick,filter_v,mode='valid')
f, axarr = plt.subplots(1,2,figsize = (50,50))
axarr[0].imshow(np.absolute(out_conv_h),cmap='gray')
axarr[0].set_axis_off()
axarr[1].imshow(np.absolute(out_conv_v),cmap='gray')
axarr[1].set_axis_off()

plt.show()

image = Image.open('brick.jpeg')
brick = asarray(image)
plt.figure(figsize=(10,10))
plt.imshow(brick)
plt.axis('off')
plt.show()

out_corr_v=signal.correlate(brick,filter_v_3d,mode='valid')
out_corr_h=signal.correlate(brick,filter_h_3d,mode='valid')

f, axarr = plt.subplots(1,2,figsize = (50,50))
axarr[0].imshow(np.absolute(out_corr_h),cmap='seismic')
axarr[0].set_axis_off()
axarr[1].imshow(np.absolute(out_corr_v),cmap='seismic')
axarr[1].set_axis_off()
plt.show()

import tabletext
data = [[1,0,-1],[1,0,-1],[1,0,-1]]
print(tabletext.to_text(data))

┌───┬───┬────┐
│ 1 │ 0 │ -1 │
├───┼───┼────┤
│ 1 │ 0 │ -1 │
├───┼───┼────┤
│ 1 │ 0 │ -1 │
└───┴───┴────┘

data = [[1,1,1],[0,0,0],[-1,-1,-1]]
print(tabletext.to_text(data))

┌────┬────┬────┐
│  1 │  1 │  1 │
├────┼────┼────┤
│  0 │  0 │  0 │
├────┼────┼────┤
│ -1 │ -1 │ -1 │
└────┴────┴────┘

Padding

Strided Convolutions

Convolutions on volumes (RGB images)

Schematic Description of a Convolutional Layer

Layers in ConvNets

The building blocks (i.e. most commonly used types of layers in CNNs)

• Convolutional layers
• Pooling layers
  • Max Pooling
  • Average Pooling
  • Global Pooling
• Dense (Fully Connected) layers

Schematic Description of a ConvNet

CNNs in Tensorflow